The art (or is it science?) of company valuation

When it comes to valuing companies, some people seem to suffer from what could be called 'reverse number blindness': if there's a lot of numbers and formulas involved, it must be good. However, as Aswath Damodaran points out, 'the test of a valuation is not in the inputs or in the modeling, but in the story underlying the numbers and how well that story holds up to scrutiny'. If the numbers you put in your valuation model do not reflect reasonable expectations about future cash flows and risk, your valuation is worthless however sophisticated your model is. Which raises the question: what are reasonable expectations? As a wise man once said: 'it's tough to make predictions, especially about the future'. When valuing a company, it is important to understand that valuations are only informed guesses, typically based on limited and (very) noisy information.

The Financial Times recently discussed an interesting illustration of this problem. In 2011, a company called Rural-Metro was acquired by private equity firm Warburg Pincus. Afterwards, shareholders sued Rural-Metro's directors for breaching their fiduciary duties, and Rural Metro's bankers - including Royal Bank of Canada - for aiding the directors in selling the company too cheaply, supposedly to get new lucrative financing assignments. While the other parties settled before a trial, Royal Bank of Canada contested the charges in a court in Delaware.

This led to a discussion about the valuation of Rural-Metro. In any discounted cash flow valuation (DCF), expected future cash flows are discounted at the cost of capital. According to the Capital Asset Pricing Model (CAPM) (basic version), the cost of equity = the risk free rate + beta x equity risk premium. In this model, beta measures the 'systematic risk', i.e. the extent to which the equity returns co-vary with the overall market return. There are two big problems with this approach. To begin with, it isn't even clear whether CAPM is a good approach to measure the cost of equity. Basically, people use it because (a) it is very simple to apply, and (b) there do not seem to be any significantly better approaches when it comes to valuation in the real world.

A second problem is that beta can be measured in different ways, and different approaches can lead to very different valuations. In the case of Rural-Metro, both parties made different assumptions with respect to beta. While they both used regression analysis and historical returns to estimate beta, the plaintiffs based their analysis on the weekly returns over a two year period, and the Royal Bank of Scotland advocated the use of monthly returns over a five year period. Both approaches are considered valid ways to estimate beta, but in this case the results were markedly different. The weekly data yielded a beta of 1.2, while the monthly data generated a higher beta of 1.454. It will probably not surprise you that the approach chosen be the parties confirmed their respective view points. The plaintiffs argued that the price at which Rural-Metro was sold was too low, which was disputed by the bank. A higher beta implies a higher cost of capital, and hence a lower DCF-valuation. The higher the DCF-value of Rural-Metro, the greater the damages to which the plaintiffs were entitled. The beta of 1.2, advocated by the plaintiffs, yielded a value of $21.42 per share, while the beta of 1.454, defended by the Royal Bank of Canada, yielded a 21% lower value of only $16.91 per share, decreasing total DCF value by no less than $100 million.

Which of these two approaches is the best? Personally, I would use neither: beta coefficients of individual stocks are often very unstable over time. You may try it yourself: calculate the beta of any stock over different periods of time, and you often end up with very different beta estimates. An extreme example is the beta of bank stocks, which for some banks exploded during the recent financial crisis. (*) A more reliable way to estimate beta is to use the mean or median 'unlevered beta' (i.e. adjusted for differences in leverage) of the industry in which the firm is operating. This is a much more stable measure, and it has been found that the betas of individual stocks tends to evolve towards industry averages.

However, the broader problem here is the reliability of DCF valuations. Any valuation will depend on the underlying assumptions, and a minor change in assumptions can lead to very different valuations. Does this mean that DCF valuations are worthless? According to Marc Andreessen, DCF valuations only serve to justify existing market valuations. I think mr. Andreessen is a bit too cynical here. (**) The big advantage of DCF valuation is that it allows to assess the assumptions on which a company valueis based. Are the underlying assumptions about the cost of capital and growth prospects in any way realistic? Let's say you would consider to buy Apple stocks: what does the current market valuation of Apple imply with respect to growth rates? DCF will help you understand this and will you help to decide whether to buy or sell Apple.

(*) Yes, I am aware that the 2007-2008 crisis was an unexpected, exceptional event, but unexpected exceptional events are basically happening all the time: any approach which does not take into account the possibility of such events is problematic in my view.

(**) Although I do like Andreessens' statement that the 'Efficient Market Hypothesis is correct if for "all information" you substitute "all information, theories, noise, and bullsh*t"'. It's a strange beast, this so-called Efficient Market.

Are stocks currently overvalued?

Many people think that stocks are currently overvalued, because price/earnings ratios are nowadays much higher than historical averages (see for example here and here). Are they right? To answer this question, let's take a closer look at the valuation of stocks. The value (V) of any financial asset is determined by expected future cash flows (CF) and the required rate of return (r), with (simplified): V = CF / r.

If stocks are currently overvalued, this may be because investors overestimate expected future cash flows, i.e. company earnings. While this is probably true for some companies (Tesla Motors comes to mind, but who knows?), it seems doubtful to me that this applies to the overall market. There is currently a broad sense of pessimism about future economic growth (cf. the secular stagnation debate) and it is often argued that firms hold too much cash and don't invest enough. Not exactly an environment in which you would expect investors to be overly optimistic about the growth prospects of firms.

So, maybe then the return required by investors is too low? The required return on stocks consists of two parts: the risk free return plus an equity risk premium which takes into account that stocks are more risky than fixed return investments. Perhaps the equity risk premium should be higher? This is also doubtful: Aswath Damodaran, who is one of the smartest guys around when it comes to valuation, calculated that the equity risk premium for S&P 500 firms did not at all decline in the past five years. And why would the equity premium currently be too low?

Is the risk free return the culprit then? At first sight, this seems to make sense: central bank policies in the US, Europe and Japan (Evil Quantitative Easing) have driven down intrest rates (well, at least that's what is generally assumed, but I'm not aware of any hard evidence on this). The risk free return can be broken down in two components: expected inflation plus the "real intrest" that investors want for parting with their money.

It could be that current risk free returns insufficiently take into account future inflation. Indeed, people have been arguing for years that the QE policies pursued by central banks wil  inevitably lead to high inflation. However, it seems very unlikely that stocks are overvalued because future inflation is underestimated. First, it is doubtful that quantitative easing will lead to high inflation. More importantly, whatever your belief about the impact of QE on inflation, inflation should not matter that much for stock returns. As I have explained in a previous post, stocks seem to provide a pretty good hedge against inflation: if inflation goes up, the firms' cash flows also go up (*). If you expect high inflation, you're better off with stocks than fixed income securities!

This brings us to the last reason why stocks might be overvalued: current intrest rates underestimate the "true" intrest rate, leading to too low discount rates. Central bank policies could temporarily have driven real intrest rates below "normal" levels, and stock investors insufficiently take into account that sooner or later real intrest rates will go up again, which will bring down the value of stocks. Here, Damodaran again provides a very useful perspective. He points out that in the long run, the real intrest rate has to backed up by a real growth in the economy. He finds that the intrest rate on US Treasury Bonds in recent decades is indeed strongly correlated with the sum of actual inflation rate and realized economic growth rate, which is a proxy for the "intrinsic" intrest rate, i.e.  the sum of expected inflation and expected real economic growth. Furthermore, this relation seems hardly to be affected by QE, at least in the US. This suggests that current real intrest rates probably provide a not-so-bad reflection of the "true" intrest rate, irrespective of QE in recent years. Now, maybe investors do underestimate the "true" intrest rate because they underestimate future economic growth, leading to a discount rate being used to value stocks that is too low. However, if this is the case, then expected future company earnings are probably also too low, implying that the value of stocks might actually be underestimated and stock prices are too low.

Bottom line: even stock valuations are currently very high from a historical perspective, there are good reasons to believe that stocks are generally not overvalued. Yes, current stock valutions are based on low discount rates, but (a) low discount rates could reflect a new "normal" (as e.g. Robert J. Gordon has pointed out, we may have entered a new era of permanent low economic growth); and (b) even if economic growth picks up again leading to higher required rates of return, this economic growth should also lead to higher company earnings, increasing the value of stocks. A final point: if stocks would be overvalued, it doesn't make sense to  shift your money to alternative investments such as bonds or real estate, if these alternatives are also overpriced.

(*) And as I always tell my students, you need be careful not to discount real cash flows (which do not incorporate expected inflation) with nominal discount rates (which do take into account expected inflation).